Templet for drawing transition spirals.



, No. 866,152. PATENTED SEPT. 17, 190v.-

J. A. MERRITT.

TBMPLET FOR DRAWING TRANSITIONSPIRALS.

APPLICATION FILED MAY 15. 1907.

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W/TNES Jam/615d. [/Vl E/VTOR BJJCZZ A A TTOPNE ys No. 866,152 PATENTEDSEPT. 17, 1907. J. A. MBR-RITT.

TEMPLET FOR DRAWING TRANSITION SPIRALS. APPLICATION FILED MAY 15. 1907.

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W/ T/VESSES JamwAMer/"EZ,

PATENT OFFICE.

JAMES ALFRED MERRITT, OF BALTIMORE, MARYLAND.

TEMPLET FOR DRAWING TRANSITION SPIRALS- Specification of Letters Patent.

Patented Sept. 17, 1907.

Application filed May 15,1907. $erial No. 373,745.

To all whom it may concern:

Be it l mown that I, JAMES ALFRED MERRIIT, a citizen ol the UnitedStates, residing at Baltimore, in the county of Baltimore City and Stateof Maryland, have invented a new and useful Templet for Drawing Transition Spirals, of which the following is aspecification.

in modern railway practice it is no longer usual to connect twoangularly related lines of road by a simple curve, and transition oreasement curves are now employed in order to gradually change thedirection of travel of the train. A transition curve or easement curve,as it is sometimes called, is a curve of varying radius used to connectcircular curves with tangents for the purpose of avoiding shock anddisagreeable lurch of trains due to instant change in the relativepositions of cars, trucks, and draw bars, and, also, to a sudden changefrom level to inclined tracks.

The primary object of the transition curve is to effect smooth ridingwhen the train is entering or leaving a curve.

The generally accepted requirement for a power transition curve is thatthe degree of curve shall increase gradually and uniformly from thepoint of tangent until the degree of the main curve is reached, allowingthe super elevation to increase uniformly from zero at the tangent tothe l'ull amount at the con-' nection with the main curve, and'yet toafford at every point the appropriate super elevation for the curvature.

The field engineer in laying out a line determines first the degree ofcurve which will best meet the requirements of cut and fill and suchother conditions as may be necessary, and the question of transitioncurves, or transition spiral, as it may more properly be termed, used toconnect the angularly related lines and circular curve, are thendetermined. In plotting these transition curves either for new trackage,or for the correction ol' old tracks, considerable difiiculty isexperienced in laying out curves that are mathematically correct, andthe present practice, which will be entered into in detail hereinafter,is only approximate and requires con siderable skill and time to workout.

The principal object of the present invention is to provide a novel formof templet, so shaped and so graduated that given a curve of anypredetermined degree, the transition spiral may be drawn without furtherdifficulty, and with out any mathematical calculations whatever and withthe utmost accuracy.

I11 the accompanying drawingsz-Figure l is a plan view of a templetconstructed in accordance with the invention. Fig. 2 is a transversesectional view of the same on the line 2-2 of Fig. 1. Figs. 3, 4, 5, 6,7, 8, 9, 10 and 11 are diagrams illustrating the outlines of templets ofdifferent contour all embodying the invention.

Figs. 12 and 13 are diagrams more particularly referred to hereinafter.

Where .two roads, such as F G, are to be united by a curve, the engineerwill, of course, try to employ a curve of the largest radius, butconditions are frequently such as to limit the choice, such, forinstance, as the cost of property to be acquired, the conditions of cutand fill, and the like, so that a curve of comparatively small radiusmust sometimes be used. One of the methods at present inuse consists inprojecting the lines F and G to a meeting point D, and then the point atwhich the curve begins is determined by the previously noted conditions,and these points, A O, are pricked, after which perpendiculars are drawnto the lines A D, D C, from the points A and C to a meeting point 0,this forming the center from which the curve B is struck. The degree ofcurve is measured in the usual manner by drawing a chord of one hundredfeet across an,arc of the curve and measuring the angle between theradii which connect the ends of the chord to the point 0.

In determining the points H M at which the circular curve ends,considerable clifliculty is experienced. One of the ordinary methods isthat followed in topographical work in polyconic projections, that is,by marking off the x values or latitude from A K on the line A D,andthen the g values from K to H, after which the point H is pricked,and marks the commencement of the circular curve. The transition spiralmust then be drawn by using the proper number of curves to complete thedistance A H, there being usually a separate curve for each 93 value.This method is very slow and expensive, and is correct only .in so farthe points measured are concerned, while the drawing is imperfect owingto the difliculty in properly joining the different curved lines.Another method is to lay off or calculate the course from a meridian,(or in a straight line, that is north and south, and going out on it adistance A H, the angle K A H being measured by a protractor and beingonly approximate.

In Fig. 12 the dotted line S represents a simple circular curveconnecting the lines F G, the curve being, say, a five degree curve.This simple curve is no longer used in railroad engineering, and in thelaying out of a new line, or in the correction of an old line, the curveis moved out, as indicated by the line T, and its ends are connected tothe lines F and G by the transition or easement spirals, each of whichmust be separately calculated.

The transition spiral is a curve whose degree of curve. increasesdirectly as the distance along the curve from the point of spiral. Thus,if thespiral is to changeat the rate of ten degrees per hundred feet, atten feet from the begining of the spiral the curvature will be the sameas that of a one degree curve; at twenty-five feet, as of a two degreethirty minute curve; at sixty feet, as a six degree curve; at eightyfeet, as an eight degree curve, etc. A spiral curve of this type wouldbe known then as a ten degree spiral.

Where a five degree circular curve is to be connected to two straightlines by a two degree thirty minute transition spiral the engineerusually plots from the point A to the point K in measuring the at valuesor latitude, and then by known rules calculates the y values ordeparture from the point K to the point H.

In order to overcome the various difiiculties of the -method and toprovide a simple method of drawing the transition spiral and locatingthe points of connection of the transition spiral and the circular curvewith the utmost accuracy, I have provided an improved templet which may.be used after the two points A C and the degree of the circular curvehave been determined upon, no further measurements or calculations beingnecessary. The templet 10 is formed of a strip of celluloid, ivory, woodor any other material, and preferably has its drawing edge beveled fromboth sides, as shown in Fig. 2, so that it may be reversed. The templetis shaped to correspond to the degree of the spiral or volute to bedrawn, the one in the present instance being calculated for a one degreespiral, that is to say, a spiral which at the end of a chord of onehundred feet from the point of the spiral is on a curve of one degree,and at two hundred feet, a curve of two degrees, and so on, the scalefollowed being marked up to one thousand feet, where the curvaturecorresponds to that of a curve of ten degrees. If the circular curve tobe used is a five degree curve, the templet is laid along the line D Gwith its straight edge u v in alinement with A G, and the zero markopposite the point A. The pricker is moved along to the five degreemark, and the point H is pricked, the point H being thus located withoutany further measurements or calculations, and at this point the spiralwill be of the proper curvature to merge into a five degree curve. Thesame operation is repeated on the line F D to locate the point M, andthen the two points H M are connected by the five degree circular curve.It will be seen that a train passing from the straight line G to thecircular curve will gradually change its position to the extent of onedegree for each hundred feet, so that when it finally reaches thecircular curve, there will be no disagreeable lurch, and the runningwill be as smooth as on a straight track. If the circular curve weresix, seven, or eight degrees, or any other degree marked on the scale,the pricker would be stopped at the proper point to join with suchcircular curve. The transition spiral to be used to connect the straightlines to the curve is determined by property lines and the requirementsof cut and fill, so that to make a complete set of measurements, it isdesirable to employ templets curved to correspond to volutes ofdifferent degrees.

In Figs. 3 to 11, which are more or less diagrammatic in form, areillustrated the outlines of templets for spirals of different curvature,that shown in Fig. 3 being for a spiral which curves at the rate oftwelve minutes or one-fifth of a degree for each one hundred feet; inFig. 4 the curvature is fifteen minutes, or onefourth of one degree; inFig. 5 the curvature is thirty minutes or one-half of one degree; inFig. 6 the curvature is forty minutes, or two-thirds of one degree; in

Fig. 7 the curvature is forty-eight minutes or fourfifths of one degree;in Fig. 8 is shown the one degree curve illustrated in Fig. 1; in Fig. 9is shown a one degree fifteen minute curve; in Fig. 10 a one degreeforty minute curve, and in Fig. 11 a two degree curve, and this set ofcurves will meet all the requirements of modern railroad practice.

I claim:

1. An instrument for drafting transition spirals, said instrument havinga drawing edge following a spiral of predetermined curvature, and beingprovided with graduations from zero representing the degree of thespiral, and characters opposite the graduations to indicate the gradualincrease in the degree of curve to thereby facilitate the location ofthe connecting point of the spiral with a circular curve.

2. A drafting instrument comprising a curve, the drawing edge of whichis straight in one direction from a zero point, and in the oppositedirection from the zero point is curved to follow a transition spiral,there being graduations along the curved portion of the drawing edge,and characters to indicate the gradually increasing degree of curvaturein accordance with the distance from such zero mark.

In testimony that I claim the foregoing as my own, I have hereto aflixedmy signature in the presence of two witnesses.

JAMES ALFRED MERRITT.

Witnesses S. SCOTT BECK, Tnoims MASSEY.

